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Geometry Lectures by Nigel Simmons

Lectures from 2014-2015 from teacher Nigel Simmons.



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Geometry Lectures by Nigel Simmons
audio
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A quick look at the generalistion of the sum & difference formulae
Topic: sum & difference formulae
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio
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General expressions for the factorising and expanding of cubics
Topics: algebra, cubic
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Differentiating a product of two functions
Topic: calculus
Geometry Lectures by Nigel Simmons
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Investigating graphs through limits
Topics: limits, calculus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Converting the product of two trig functions inti a sum, and visa versa
Topic: trig
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Using integration to find volumes
Topics: integration, volumes
Geometry Lectures by Nigel Simmons
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Looking at the initial angle theorems.
Topics: circles, angle theorems, euclidean geometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Describing the parabola geometrically and deriving the algebraic form.
Topics: parabola, locus
Geometry Lectures by Nigel Simmons
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Using the derivative to solve rates of change problems
Topics: calculus, rates of change
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Working with surds
Topic: surds
Geometry Lectures by Nigel Simmons
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What if some of the objects are the same?
Topic: permutations
Geometry Lectures by Nigel Simmons
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Looking at the relationship between the roots and coefficients ofa polynomial
Topic: polynomials
Geometry Lectures by Nigel Simmons
audio
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Reducing equations to quadratics in order to solve.
Topic: quadratic
Geometry Lectures by Nigel Simmons
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looking at number patterns
Topic: series
Geometry Lectures by Nigel Simmons
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Finding the means of numbers
Topics: series, means
Geometry Lectures by Nigel Simmons
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Finding the area under a curve
Topics: integration, area
Geometry Lectures by Nigel Simmons
audio
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How to find the equation of a line that passes through the point of intersection of two given lines and another point.
Topics: linear function, lamda formula
Geometry Lectures by Nigel Simmons
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Find the equaio ofthe chord of contact
Topic: parabola
Geometry Lectures by Nigel Simmons
audio
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Defining and proving the irrationality of numbers
Topic: irrational
Geometry Lectures by Nigel Simmons
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Solving optimisation problems using calculus.
Topics: calculus, maxima, minima
Geometry Lectures by Nigel Simmons
audio
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Finding the equation of a line that pase through the intersection of two given lines and another point.
Topics: linear function, lamda formula
Geometry Lectures by Nigel Simmons
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Using first principles to come up with a rule for differentiating polynomial functions.
Topics: calculus, differentiation
Geometry Lectures by Nigel Simmons
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Inequalities are represented by regions when placed on the number plane.
Topics: algebra, curve sketching, inequalities
Geometry Lectures by Nigel Simmons
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Deriving the equatiuon of te chord of contact
Topics: parabola, chord
Geometry Lectures by Nigel Simmons
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Solving problems using calculus
Topic: calculus
Geometry Lectures by Nigel Simmons
audio
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Key features to look for when sketching polynomials
Topics: polynomials, curve sketching
Geometry Lectures by Nigel Simmons
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Solving trig equations
Topics: trigonometry, trig equations
Geometry Lectures by Nigel Simmons
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Introducing sigma notation
Topics: series, sum
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Calculating areas if irregular shapes
Topics: integration, areas
Geometry Lectures by Nigel Simmons
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Solving equations (and inequations)
Topics: equations, inequations
Geometry Lectures by Nigel Simmons
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The basic algebraic operations
Topics: algebra, indices
Geometry Lectures by Nigel Simmons
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Inequalities involving two variablss
Topic: regions
Geometry Lectures by Nigel Simmons
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Defining functions and finding domain and range
Topics: functions, domain, range
Geometry Lectures by Nigel Simmons
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Finally a look at the inequality type of induction problem
Topics: induction, inequality
Geometry Lectures by Nigel Simmons
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Sketching polynomials by looking for key details in the equation
Topics: polynomial, curve sketching
Geometry Lectures by Nigel Simmons
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Defining the quadratic and how to find its important features.
Topics: quadratic, curve sketching
Geometry Lectures by Nigel Simmons
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Properties of quadrilaterals
Topics: geometry, quadrilaterals
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio
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Looking at the specific case of the locus as a parabola
Topics: parabola, locus
Geometry Lectures by Nigel Simmons
audio
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The basic definitions of circke properties and introducing some chord (arc) theorems.
Topics: euclidean geometry, circle, chord theorems
Geometry Lectures by Nigel Simmons
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The alternate segment
Topic: alternate segment
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Expanding on the idea of transforming the basic curves.
Topic: curve sketching
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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the primitive function
Topics: calculus, primitive function
Geometry Lectures by Nigel Simmons
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Calculating a series
Topic: series
Geometry Lectures by Nigel Simmons
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The properties of quadrilaterals become more specialised as you branch down the "family" tree.
Topics: geometry, quadrilaterals
Geometry Lectures by Nigel Simmons
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When two quadrtics are "congruent", the coefficients an be matched.
Topics: quadratic, identities
Geometry Lectures by Nigel Simmons
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The first of the angle theorems
Topic: circle geometry
Geometry Lectures by Nigel Simmons
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Techniques for solving basic equations/
Topics: algebra, equations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Defining te sine rule for use in non-right angled triangles, as well as a formuls for finding the area of a triangle without having to know the perpendicular height.
Topics: trigonometry, sine rule, area
Geometry Lectures by Nigel Simmons
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Three diferent levels of inequality questions
Topic: inequations
Geometry Lectures by Nigel Simmons
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How to find areas for functions too difficult to integrate
Topic: integration
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Deriving the sine rule
Topic: trigonometry
Geometry Lectures by Nigel Simmons
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Looking at a couple of unusual questions
Topic: dynamics
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Deriving the double angle formulae
Topics: trigonometry, double angles
Geometry Lectures by Nigel Simmons
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A couple of questions that have appeared in the past years
Topic: induction
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Newton's method
Topic: approximation
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the valueof integrals for curves that can't be integrated!!
Topics: integration, approximations
Geometry Lectures by Nigel Simmons
audio
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Some alternative ways of finding the features of quadratics
Topic: quadratic
Geometry Lectures by Nigel Simmons
audio
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Manipulating the roots of unity
Topics: complex numbers, roots of unity
Geometry Lectures by Nigel Simmons
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Raising complex numbers to powers
Topics: complex numbers, de moivres
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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A regular question in the Extension 2 paper involves circle geometry
Topics: harder extension 1, circle geometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio
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Defining the family of conics and more specifically, te ellipse.
Topics: conics, ellipse
Geometry Lectures by Nigel Simmons
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Sketching functions on the complex plane
Topics: complex numbers, locus
Geometry Lectures by Nigel Simmons
audio
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Defining the parametric coordinates of the ellipse and finding the tangent and normal.
Topics: conics, parmeters, ellipse
Geometry Lectures by Nigel Simmons
audio
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Lines & rays in the Argand diagram
Topics: complex numbers, locus
Geometry Lectures by Nigel Simmons
audio
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The parametric form of the ellipse
Topics: ellipse, parameters
Geometry Lectures by Nigel Simmons
audio
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Extending the relationship between roots & coefficients
Topic: polynomials
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio
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Factorising over rtge complex field
Topic: polynomials
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio
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Investigating roots of higher multiplicity
Topic: polynomials
Geometry Lectures by Nigel Simmons
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Expanding on the idea from Extension 1
Topics: polynomials, roots, coefficients
Geometry Lectures by Nigel Simmons
audio
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Transforming a special hyperbola
Topic: hyperbola
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio
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The product rule for integration
Topics: integration, by parts
Geometry Lectures by Nigel Simmons
audio
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Sketching curves that are a composition of two (or more) functions.
Topic: curve sketching
Geometry Lectures by Nigel Simmons
audio
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A hyperbola whose asymptotes are perpendicular
Topics: conics, hyperbola
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio
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Expressing acceleration in different ways
Topic: acceleration
Geometry Lectures by Nigel Simmons
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Investigating the forces involved in circular motion
Topic: circular motion